Equilibrium expression charge balance

You should be able to describe a system at equilibrium both qualitatively and quantitatively. Rigorous solutions to equilibrium problems can be developed by combining equilibrium constant expressions with appropriate mass balance and charge balance equations. Using this systematic approach, you can solve some quite complicated equilibrium problems. When a less rigorous an-... 

Table 16-2 List of input components for the simplest case of the acid-base balance of unpolluted marine clouds. Also shown are the mass conservation statements, chemical equilibrium expressions and constants, and the requirement for charge balance...

The general treatment of acid-base systems begins with charge and mass balances and equilibrium expressions. There should be as many independent equations as chemical species. Substitute a frac-... 

The equilibrium pH can be obtained directly from the log ra. pH plot by adding lines showing log H and log OH and by using an expression for charge balance. 

For a solution containing a weak acid, the charge balance relationship (3.47) is satisfied at the equilibrium pH (Example 3.5). The same log vs. pH plot can also be used to determine the equilibrium pH of a solution containing the salt of a weak acid, e.g. NaA, by using the appropriate charge balance expression. 

The equilibrium pH for a solution containing the weak acid is obtained by approximating the charge balance expression by H TCP (because the solution will be acidic and thus OH is very small). Conversely, the equilibrium pH for a solution of the salt of the weak acid is obtained by approximating the appropriate charge balance expression by TCP OH (because the solution will be basic and so H is very small). 

The slopes for the other lines are obtained in the same way. Approximating the charge balance expression (3.62) by H" HC03 gives the equilibrium pH for a closed aqueous system containing carbonic acid. 

Alkalinity is an important parameter in assessing the elfects of environmental change on aqueous systems (see Section 3.3.4.1). It is also important to understand that, by definition, alkalinity (Equation (3.61)) is independent of addition or removal of CO2 (or H2CO3) from the system (c/ Equation (3.62) - H2CO3 does not appear in the charge balance expression). This can be very useful in the determination of the concentration of dissolved inorganic carbon species in aqueous systems that are in equilibrium with an atmosphere containing C02(g) (Example 3.7). 

Plotting —log V5. pH for HC03 and C03 gives lines of slope +1 and +2, respectively. The charge balance expression, which is the same as that for the closed system, can again be used to determine the equilibrium pH. 

WATEQ2 consists of a main program and 12 subroutines and is patterned similarly to WATEQF ( ). WATEQ2 (the main program) uses input data to set the bounds of all major arrays and calls most of the other procedures. INTABLE reads the thermodynamic data base and prints the thermodynamic data and other pertinent information, such as analytical expressions for effect of temperature on selected equilibrium constants. PREP reads the analytical data, converts concentrations to the required units, calculates temperature-dependent coefficients for the Debye-HKckel equation, and tests for charge balance of the input data. SET initializes values of individual species for the iterative mass action-mass balance calculations, and calculates the equilibrium constants as a function of the input temperature. MAJ EL calculates the activity coefficients and, on the first iteration only, does a partial speciation of the major anions, and performs mass action-mass balance calculations on Li, Cs, Rb, Ba, Sr and the major cations. TR EL performs these calculations on the minor cations, Mn, Cu, Zn, Cd, Pb, Ni, Ag, and As. SUMS performs the anion mass... 

Three types of algebraic equations are used in solving multiple-equilibrium problems (1) equilibrium-constant expressions, (2) mass-balance equations, and (3) a single charge-balance equation. We showed in Section 4B how equilibrium-constant expressions are written we now turn our attention to the development of the other two types of equations. 

This equation represents the charge-balance condition and is called the charge-balance equation. To be useful for equilibrium calculations, the equality must be expressed in terms of the molar concentrations of the species that carry a charge in the solution. 

Approximations can be made only in charge-balance and mass-balance equations—never in equilibrium-constant expressions. 

Bear in mind that only the mass-balance and charge-balance equations can be simplified because only in these equations do the concentration terms appear as sums or differences rather than as products or quotients. It is always possible to assume that one (or more) of the terms in a sum or difference is so much smaller than the others that it can be ignored without significantly affecting the equality. The assumption that a concentration term in an equilibrium-constant expression is zero makes the expression meaningless. 

If we do not know the pH, the logarithmic concentration diagram can also be used to give an approximate pH value. For example, find the pH of a 0.1 M maleic acid solution. Since the log concentration diagram expresses mass balance and the equilibrium constants, we need only one additional equation such as charge balance to solve the problem exactly. The charge-balance equation for this system is... 

To derive a function for the buffer index of a weak monoprotic acid, HA, we begin as before with equilibrium, mass-balance, and charge-balance equations, and first derive an equation for the titration curve. We are given the following expressions ... 

It is useful to construct a graph relating carbonate mineral solubilities to CO2 pressure. This can be done for calcite starting with equilibrium constant expression (6.2) above. If done rigorously, the derivation accounts for the effects of ion activity coefficients and the presence of CaHCOI and CaCOf ion pairs and of CaOH. Considering all complexation, the exact charge-balance equation for a pure water in which calcite is dissolving is... 

Knowledge of for a weak acid (or Kb for a weak base) facilitates estimation of the concentrations of the various species after equilibrium is established. When accurate solutions for equilibrium concentrations of a weak acid, for example, are required, the exact approach requires solving four simultaneous equations. Two of these have already been discussed, one being the acid ionization expression of equation (22), and the other being the water dissociation expression of equation (15). The third necessary equation is the charge balance equation ... 

Various empirical and chemical models of metal adsorption were presented and discussed. Empirical model parameters are only valid for the experimental conditions under which they were determined. Surface complexation models are chemical models that provide a molecular description of metal and metalloid adsorption reactions using an equilibrium approach. Four such models, the constant capacitance model, the diffuse layer model, the triple layer model, and the CD-MUSIC model, were described. Characteristics common to all the models are equilibrium constant expressions, mass and charge balances, and surface activity coefficient electrostatic potential terms. Various conventions for defining the standard state activity coefficients for the surface species have been... 

Use equilibrium constant expressions plus mass and charge balance expressions to write the equations. 

There are three unknowns ([AB], [A" ], and [B ] the concentration of M" is known to be 0.20 M) and three independent expressions (one equilibrium and two mass balance the charge balance is the same as the second mass balance). 

We may solve the multiple equilibrium problem as well by using the systematic The systematic approach is well approaches described in Chapter 6, using the equilibrium constant expressions, the suited for competing equilibria mass balance expressions, and the charge balance expression. calculations. 

Fig. 5 shows the results of both titration experiments. The experimental results are in good agreement with the predictions based upon the equilibrium expressions for Kb the Ka for each indicator, and the mass and charge balances[13]. The data from the acid titration show a sharp equivalence point at approximately 10 m HCl, which suggests that B(OH)4 is still a strong base at 350°C and 0.622 g/mL and capable of neutralizing HCl. This strong acid base titration curve, as was also observed for HCl and KOH, may be contrasted with the weak acid-base behavior observed for the sulfuric acid-ammonia system at 380 C[41]. 

In general it can be shown that exactly enough internal defect equilibria exist to permit us to express all defect concentrations as functions of the independent variables, as long as the material, site, and charge balances are observed. This explains the free choice which we have in formulating eq. (4-5) (i.e. in formulating the external equilibrium conditions). 

Substitution of equilibrium constant expressions into the material or charge balance equation for solubility can give correct equations for solubility as a function of H and/or complexing ligand concentrations. 

The equilibrium constant expressions above give us four equations involving six unknown concentrations [H3PO4], [H2P04 ], [HP04 ], [P04 ], [HaO" ], and [OH ]. We need two additional equations. We get them by writing a material balance equation and a charge balance equation. 

With the four equilibrium consfant expressions, a material balance equation and a charge balance equation, we have six equations involving six unknowns. In principle, this system of equations can be solved to find the six unknown concentrations, either by making appropriate simplifying approximations or by computerized calculation. 

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